July, 1963
THERMODYNAMIC DATAFOR ACETYLACETONE IK MIXEDSOLVESTS
1447
COORDINATION COMPOUNDS. VI. DETERMIXATION OF THERMODYNAMIC DATA FOR ACETYLACETONE I N MIXED SOLVENTS BYPHILIP S. GEXTILE,MICHAELCEFOLA, Department of Chemistry, Fordham University, Bronx 68, N . Y . AXD ALFRED V.
CELIANO
Department of Chemistry, Seton Hall University, South Orange, X. J . Received November 19, 1962 Thermodynamic data for acetylacetone have been determined in mixed solvents by standard methods. On the basis of a mathematical model, functions of the stability constant a t constant temperature and constant dielectric constant have been defined and evaluated. The thermodynamic data obtained by both methods are in good agreement.
Introduction I n a previous communication1 the thermodynamic dissociation constants of acetylacetone in two and three component solvent systems a t 25' were reported. It was found that these dissociation constants were related linearly to the reciprocal of the dielectric constant of the solvent and were independent of the nature of the solvent in the dielectric range 80-30. I n this paper the dissociation constants of the same ligand in methanol-water and dioxane-water mixtures are reported, as well as a method of evaluating the standard free energy, enthalpy, and entropy of ionization. It has long been recognized that the effect of temperature on the ionization constants of acids is not only related to the energy required to break the chemical bond and the energy of solvation but is also related to the work done in separating the solvated charged products to their equilibrium distances. The latter electrical work was considered by Born2 on the basis of elementary electrostatic theory. Another approach may be found in the Bjerrumarid Ramsey5 have Fuoss ion-pair m ~ d e l . ~Denison .~ simplified the original concept by assuming that two oppositely charged ions exist either in contact as an associated ion-pair, or a t such a large distance apart that the coulombic force between them is negligible. I n evaluating the thermodynamic quantities associated with ionization, both the chemical and electrical factors must be taken into account. Much of the work done up to the present has involved the determination of ionization constants in a single solvent or solvent system. The variation of pK with temperature is then employed to calculate the total AFO, AHo, and ASo and the electrical parts of these quantities are then calculated on the basis of a theoretical model, more or less complex. Such an approach has been considered invalid by Harned and Owen,G primarily because the solvent in a system containing ions is not a uniform medium of unvarying dielectric constant. It is considered in this paper, however, that if the dissociation constants were determined a t various temperatures and in mixed solvents of varying dielectric constants, then both the chemical and electrical thermodynamic (1) P. S. Gentile, M. Cefola, and A. V. Celiano, J . Phys. Chem., 67, 1085 (1963). (2) XI. Born, Z. Phyaik, 1, 45 (1920). (3) J. Bjerrum, Ko1. Danske Videngkab Selskab., 7, No. 9 (1926). (4) R. M. Fuoss and C. A. Kraus, ,I. Am. Chem. SOC.,66, I019 (1933). (5) J. T. Denison and J. B. Ramsey, ibzd., 77, 2616 (1955). (6) H. S. Harned and B. B. Owen, "The Physical Chemistry of Electroy tic Solutions," Reinhold Publ. Carp., New York, N. Y., 1958.
quantities might be determined without consideration of a particular model, Le., on the basis of a purely mathematical separation of these terms. Such information would be useful for the correlation of data already present in the literature on the stability of chelates, where choice of solvent system so often depends on the solubility of chelating agents, metal salts, and the resulting chelate compound. The approach outlined above, Le., the purely mathematical separation of thermodynamic quantities, is based on two assumptions; first, that the change in solvent composition does not appreciably change the basic strength of the mixed solvent employed in this study. This assumption seems warranted when we consider the linear relationship between pK and 1/D at a given temperature. Second, that as solvent mixtures vary there is no preferential solvation by the solvent present in excess. Fuoss' considered the same problem in dealing with the purely electrostatic factors affecting ion pair formation and concluded that constancy of solvation appears to be a safe assumption. Experimental The experimental procedure and the data obtained a t 25" for acetylacetone in various mixed solvents have been described elsewhere.' Additional data for the same systems for use in this paper were obtained a t 0 and 40".
Results The solvents used were methanol-water and dioxanewater mixtures because activity coefficients are givens only for these particular mixtures a t three different temperatures (0,25, and 40'). Representative values of pK for acetylacetone (pK = -log Ka), which will be used in the discussions are listed in Table I, and these plus additional pK values are plotted against 1/D in Fig. 1. The equations for the linear portions of the lines in Fig. 1, Le., from values of 1/D between 0.01 and 0.03, determined by the method of least squares are
+ 7.89 a t 0' + 7.99 at 25' 67.9(1/0) + 8.00 at 40'
pK = 104.7(1/0) pK = 77.0(1/0)
(1)
pK
(3)
=
(2)
These equations represent the experimental data within +0.02 log unit. All subsequent discussion is limited to the region of linearity between pK and 1/D. The (7) R. M. Fuoss and C. A. Kraus, J . Am. Chem. Soc., 79,3304 (1957). (8) Reference 6, p. 726 ff.
P. S. GENTILE,31. CEFOLA,AND A. V. CELIANO
1448
System no.
1
I1 111 IV
V VI
%
1/D
PK
1/D
PK
1) D
PK
0.00 35.98 45.66 54.15 65 82 21 36
0.01135 ,01440 01557 ,01669 ,01862 ,01481
9.07 9.40 9.51 9.62 9.82 9.41
0.1273 ,01623 ,01763 ,0189'7 ,02118 ,01672
8.97 9.22 9.38 9.47 9.63 9.25
0.01367 ,01757 .01904 ,02061 ,02320 ,02631
8.90 9.15 9.27 9.40 9.57 9.75
Solvent system
Water Methanol-Water Methanol-Water Methanol-Water Methanol-X'ater Dioxane-Water
At first glance one might suspect that AHois a function of temperature because AC, is a function of temperature. However, according to Pitzerll and Everett and Wynne-JonesI2 AC, is independent of temperature for many acid dissociation reactions. If such be the case for the dissociation of acetylacetone, one might then explain the observed non-linearity of pK us. 1/T solely on the basis of the temperature coefficient of the dielectric constant and its effect on pK. This, however, is equivalent to stating that in the present case pK is a function of temperature and dielectric constant and is independent of the nature of the solvent system. Therefore
I I .6-
11.2 10.810.4J Q
10.0-
9.6-
pK I
0.01
1701. 67
0.02
I
1
0 03
004
=
f(D,T)
(5)
~
I I D.
Dividing through by dT
Fig. 1.-pK values plotted against 1/D: 0, water; 0 , methanolwater; A, dioxane-water.
method of least squares was utilized in all calculations. ,411 thermodynamic values are for the process of ionization. Evaluation of AHo.-A plot of pK us. 1/T for a particular solvent system (I, 11, etc.), the classical method for evaluation of AHo, proves to be non-linear between 0 and 40'. For an exact calculation of AHO, one may employ the treatment of Douglas and Crockf~rd.~The resulting equation is
RTlTz In (KdKd (4) Tz - Ti WaldelO has developed an equation to include higher powers of T . Thus, it was shown that whether AHo is a linear, quadratic, cubic, or quartic function of the temperature, equation 4 can still be used to calculate AHo from the values of K and the two corresponding temperatures. The data in Table I were treated in this manner. Values of pK a t 0 and 40' were employed since any other combination would decrease the accuracy of the calculated AHo. The AHTOvalues calculated from eq. 4 are those for the temperature, T = 292.3'K., and are listed in Table IT'. They are reliable only to i 4 0 0 cal. mole-l. Since AHo is only known at this temperature with any degree of accuracy, it is impossible to calculate ASo, since AFa can only be calculated if the constants in Walde's equation are known. This approach can, therefore, only yield a limited amount of thermodynamic data for an individual solvent system.
is obtained. But dpK - - A H o dT 2.303RT2
where AH' is the standard enthalpy change and R is the gas constant. Equation 8 therefore becomes
(T)
(9)
2.303RT2 dPK
AHT' =
(9) T.B. Douglas and H. D. Crookford, J . Am. Chem. Soc., 17, 97 (1885)' (10) A, W. Walde, J , Phyr. Chem,, 48, 431 (1888).
(8)
D
An examination of eq. 9, which results from a purely mathematical treatment and is independent of any theory, reveals that the AHo of a reaction consists of two heat terms, A&+' and AQDO, which we shall define as
(D>
= 2.303RT2 bpK
T
dD dT
(10)
and
(F)
AQDO E 2.303RT2 bPK
D
and
AH'
= A&$
+ AQDO
(11)
(12)
It is, therefore, possible to evaluate the influence of temperature or dielectric constant alone on the heat of (11) K. 9. Pitzer, J . Am. Chem. Soc., 69, 2365 (1837). (la) D. H. Everett and W, F. K, Wynne-Jones, Trans. Faraday Sac.. 86, 1380 (1939).
THERMODYNAMIC DATAFOR ACETYLACETONE IX MIXEDSOLVENTS
July, 1963
reaction, by employing eq. 10 and 11, the sum of which should give the same value for AHo, as that determined by Crockford's method. Evaluation of A&O.-FOr a given temperature and given solvent system, D and dD/dT can be obtained from the data of ikerlof and S h 0 r t . 1 ~ The ~~ expression (dpK/dD)T is obtained by differentiation of equations similar to eq. 1, 2, and 3, with respect to D. The derivative will be -c/D2, where c is the appropriate coefficient of 1/D. AQ+ approaches zero as D approaches m . Evaluation of AQDo.-Since the term ( d p K / d T ) ~in eq. 11 is a function of the dielectric constant, it is necessary to calculate isodrelectric pK values of acetylacetone at several different temperatures. This may be done visually by drawing a vertical line at any desired dielectric in Fig. 1 and evaluating pK values from curves I, 11, and 111. h more accurate method, and the one used in these calculations, is to solve eq. 1, 2, and 3 for the pK value by substituting the same dielectric constants into the three equations. Representative pK values are listed in Table I1 and are plotted against l / T in Fig. 2. From the calculated slopes of these lines (apK/dT)D may be evaluated and substituted into eq. 11 to give the AQD' values. Since in Fig. 2 pK is linear with respect to 1/T for isodielectric solvents, it follows that AQDO, the heat of the reaction at a given dielectric constant, is invariant over the ternperature range 0 t o 40'. This implies that AC, is in fact independent of temperature over the same temperature range, as predicted earlier.
1449
1 8-t-T-l 31 32
I
34
33
I /T
x
I
35 io4.
I
1
36
37
Fig. 2.-Isodielectric pK values plotted against 1/T (values given are those for l/D): 0, 0.01135; 0, 0.01440; 0 , 0.01557; A, 0.01669; A, 0.01862; 0,0.01481; . , 0.02109.
compare the values determined by Crockford's method,
ie., AHT' at 292.3'K., with those determined by eq. T ~ B LI1 E p K VALLESOF ACETYLACETONE AT REPRESENTATIVE DIELECTRIC 12. In order t o accomplish this, A&' and A&' must be evaluated for the solvent systems studied and for CONSTA~TS PK 1/D
(00)
0 01135 01440 01557 01669 01862 01481 02109
9 08 9 40 9 52 9 64 9 84 !J 44 10 10
PK
PK (250)
(SO0)
8 9 9 9 9 9 9
8 8 9 9 9 9 9
87 10 19 28 42
13 62
77 98 06 13 26 01 43
AQDO and its Relationship to Dielectric Constant.Values for AQD were calculated as described above and are themselves linearly related to 1/D. The equation for this line which is independent of temperature for 0 to 40' was determined to be A&no = 3.684 X 1Oj
(h)
- 1155 cal./mole
(13)
The value -1155 cal. per mole is a A&' extrapolated to infinite dielectric constant and is the value of the standard enthalpy change at iiifinite dielectric constant, since A&TO -+ 0 when D 4 m . This experimental fact supports the assumption of Baughaii'j and GurneyT6 that (AHO)D = is independent of temperature. Table I11 lists the A&', A&$, and AHo, calculated from eq. 9, for solvent systems I through TI. These values are reliable to f100 cal. mole-l. Reliability of AHo Values.-In order to determine the reliability of AHo values calculated by eq. 12 one must (13) G. Akerlof. J . Am. Chem. Soc., 64, 4126 (1932). (14) G. Akerl6f and 0. A Short, zbzd., 68, 1241 (1936). (16) E. C. Baughan, J. Chem. Phya., 6, 499 (1938). (16) R. W. Gurney, zhzd., 7, 951 (1930).
the temperature 292.3'K. Since AQDO is independent of temperature, this term may be evaluated directly from eq. 13, using the dielectric constant of solvent systems I-TrI at 292.3'K. &TO is evaluated by coiistructiiig a graph of pK vs. 1/D for 292.3'K. This curve m8s not determined experimentally but was evaluated from the isodielectric curves in Fig. 2 at the appropriate temperature. The resulting curve of pK us. 1/D is linear, as those in Fig. 1, and obeys the equation pK
=
84.7
($) + 7.96, at T
=
292.3'K.
(14)
AQTO was then calculated from eq. 10. The values of A H o determined by the two methods
are compared in Table IV. The excellent correlation between AHo values determined by the two methods lends support to the feasibility of separating AHo into the terms AQDO and AQTO. Evaluation of AXo.-AFn is related to the pK by the equation AFo
=
2.303RT pK
(15)
Since it has been shown that pK is linearly related to l / D (eq. 1-3), AFo is similarly related to 1/D. The equations for AFO are
1430
Vol. 67
IT I11
IC'
v
\'I
2 . (i
3.0
-4.:1
2,3
-8.1
AIP
AQTO
AQUO
A €10
3.0 -1 . 2 4 ti
1.1
-1.8
3 .5
1 .!I
-2.d
4.8
2.1
-2.4
4 :1
-2.8 -3.2 -3.7 -2.7
5.3 .i , S 6.7 5,0
I .7 2 .:3 2,,i
d(J1.0
I
AUTO -1.9 -2.9 -3.2 -3.7
AYI)~
-1.9 -2.3 -2.5 -2,s - ;1 . :I
yysfltlll
.-
2.2 2.4 I .!)
h 0 0. 1
AQDO
AH0
3.9 5.3 5.5 6.4 7.4 5.0
2.0 2.4 2.6 2.7 :3, 1 2 4 ,
'rAF%l>l'; I\'
S'I'AND.\I~I)
Hs.irr 01"Iosrz.\'Piozr, AI1 ACE;TYI.A(:IC'I'OSIs: .\TI !).
( K ( : < I ~ . - ~OF )
I
Sol1/D
AQTO
AVI)O
(AHo)"
(A/P)*
0.01240 ,01575 ,01706
-1.9
3 ,4 4.6
1.5 2.1 2.3
2.1
vent
I
-2.5 -2.8 IV .018.+1 -3.2 v ,02053 - 3 .7 YI .01u2:3 -2.7 a Cnl(:ul:Lted f r o m eq. !I. method. I1 111
1.5
5.1 5 , (i K4
2.4
2.7
2 3 2.4 2 ,5
'1 . x
2. I
2.1
(22)
,
C:LI(:ul;ttetl froin Crorkforti'n
The evaluation of ASDO aiid ASTO is complctcly aiialogous to that of AQD" and A&O. ASI," is indrpeiidcnt of
TABLE V STANDARD ENTROPIES (CAI.. Solvent system
I I1 111 IV
V VI AZf'"2'u29~.2 =
ASTO
-
6.9 8.3 9.2 -10.4 -11.9 - 8.8
ASDO
AS0
-30.4 -27.8
'Otlll
-37.3 -36. I --:36.0 -:3Ci.3 -?A. I -36.3
-26.8 -25.9
-24.2 -2 7 . 5
[ (b) + 105.1
-
00
c -
rMn1.E-1 DEQ. -1) OF 7 -
ASTO
-
6.1 8.5 9,s 10,s -12.4 - 9.0
-
IOSITATION O F ACETYLACETONE
-
250 ASDQ
ASo total
-29.3 -26.3 -25.1 -23.9 -22.1 -25.9
-35.4 -34.8 -34.6 -34.7 -34.5 --34.!)
ASTO
-
6.1 9.2 -10.2
-
-11.8
-13.8 - 9,s
40' ASDO
-25.5 -25.1 -23.0 -22.5 -20 .:3 -24.7
ASo m t a ~
-34.6 -34.3 -34.1 -34.3 -34.1
-?J4.5
temperature aiid bears a linear relationship to the reciprocal of t'he dielectric constant, expressed by the equatio 11
10.91 X lo3 cal. mole-'
(17) A P U ; ~=. ~
[ (i)+ 11.51 97.4
X lo3 cal. mole-1
(18) A S ' may bc calculated from tlic tcrnperature cocfficiciit of AI
